Most websites which dance around the anti-gun view conflate homicides with suicides to fluff up the numbers. At least this website is upfront about doing so. Who here really thinks banning guns will stop suicides?
Banning guns wouldn't completely stop suicides any more that it would completely stop homicides. But it would almost certainly push suicide rates down. If you look at age-adjusted suicide rates, they're highest in:
WY, AK, MN, NM, UT, CO, ID, NV, OR, and OK. They're lowest in NJ, NY, MA, RI, MD, IL, CT, CA, GA, and TX.
Now look at gun ownership by state:
http://usliberals.about.com/od/Election2012Factors/a/Gun-Owners-As-Percentage-Of-Each-States-Population.htm
You'll see that in the states with the highest gun ownership, the top three are identical to the top three for age-adjusted suicide. Every one of the high suicide states is in the category of extremely high, high, or median gun ownership. At the other end, of the ten low-suicide states, eight have below-median gun ownership, one median, and only one high (none are "extremely high").
Is this correlation between high gun ownership and high suicide a coincidence? I don't think so. There may be multiple factors there, but the guns themselves almost certainly factor in. When you have a gun on hand, even a moment's suicidal impulse is enough to end your life, with a very high degree of certainty. If your depression passes the threshold of "suicidal" for even a few seconds, it's enough to grab the gun, aim it, and pull the trigger, and it's all over. By comparison, to kill yourself when there isn't a gun nearby, your depression has to be beyond that suicidal threshold for longer -- the time needed to walk to a bridge and jump off, the time needed to sit in a running car parked in the garage until you fall asleep, the time for the pills you swallowed to absorb into your system before you call for help, etc. There is more time to reconsider. And with some methods, there's also the shock of pain to change your mind, and the possibility of failing and then deciding not to try again. Guns make suicide very quick, very convenient, and quite certain. And so it's only sensible to think that policies that lower gun ownership will tend to drive down suicide rates, other things being equal.
Of course, other things aren't equal. There are lots of factors to consider. For example, higher-latitude places tend to have higher suicide rates (explaining Alaska and Montana), and certain cultures have more of an affinity for suicide (e.g., certain shame-based Asian cultures). So, I'm not suggesting a one-to-one correlation between suicide and guns. But I am saying that when you pursue policies that put more guns in the mix, you should expect higher suicide rates, and that this is rightly a matter to consider when deciding the issue of gun control.